Homework Help is Here – Start Your Trial Now!
Engineering
Mechanical Engineering
The problems are generally based on the following model: A particular spacecraft can be represented as a single axisymmetric rigid body B. Let n₂ be inertially fixed unit vectors; then, 6, are parallel to central, principal axes. To make the mathematics simpler, introduce a frame C where n₂ = ĉ₁ = b; initially. 6₁ Assume a mass distribution such that J =₁₁• B* •b₁ = 450 kg - m² I = b² •Ï¾˜ • b₂ = b¸ •Ï¾* •b¸ = 200 kg - m² K J-I C³ =r₁₁ = r₁₁ Assume that the body moves in a circular orbit at a constant rate Q. Let â₁ be orbit-fixed unit vectors where a₂ is directed from the orbit center to B*; then â³ is 90° from a₂ in the direction of motion and â₁ is parallel to the orbit normal. ده * The dependent variables in the differential equations that govern motion include the measure numbers ₁; the kinematic variables that are the body 1-3-2 angles for orientation of C in A: @₁ = 0 w₂ = -Kw₁₂-rw₁₂+3KQ² (c₁₂S¸ − c₁₁ ) (c₁₁₁ + §¸§₁ ) w₁ = Kw₁₂+rw₂ −3KQ² (c₁S₂c₁₂ + $₁₂S₁) c₁₂ Ġ₁ = [(@₁c¸ + @¸§¸ − rc³)/2] - Ω ė₁₂ = − (@₁ − 1 ) s³ + W₂cz - - Ò¸ = {[@¸¢¸ − r¢¸+@₂$¸ ] $₂ / €₂ } + @₂ $2 The motion of interest is a constant spin of B in N about an axis parallel to the orbit normal, i.e., ³ = @â₁ = nÒâ₁, for some given n. Select 7 appropriately to keep C fixed in A during the nominal motion. If r = x2, what is the proper choice of x? Why? What is the resulting particular solution of the differential equations that corresponds to the nominal motion? Demonstrate that it satisfies the differential equations.

The problems are generally based on the following model: A particular spacecraft can be represented as a single axisymmetric rigid body B. Let n₂ be inertially fixed unit vectors; then, 6, are parallel to central, principal axes. To make the mathematics simpler, introduce a frame C where n₂ = ĉ₁ = b; initially. 6₁ Assume a mass distribution such that J =₁₁• B* •b₁ = 450 kg - m² I = b² •Ï¾˜ • b₂ = b¸ •Ï¾* •b¸ = 200 kg - m² K J-I C³ =r₁₁ = r₁₁ Assume that the body moves in a circular orbit at a constant rate Q. Let â₁ be orbit-fixed unit vectors where a₂ is directed from the orbit center to B*; then â³ is 90° from a₂ in the direction of motion and â₁ is parallel to the orbit normal. ده * The dependent variables in the differential equations that govern motion include the measure numbers ₁; the kinematic variables that are the body 1-3-2 angles for orientation of C in A: @₁ = 0 w₂ = -Kw₁₂-rw₁₂+3KQ² (c₁₂S¸ − c₁₁ ) (c₁₁₁ + §¸§₁ ) w₁ = Kw₁₂+rw₂ −3KQ² (c₁S₂c₁₂ + $₁₂S₁) c₁₂ Ġ₁ = [(@₁c¸ + @¸§¸ − rc³)/2] - Ω ė₁₂ = − (@₁ − 1 ) s³ + W₂cz - - Ò¸ = {[@¸¢¸ − r¢¸+@₂$¸ ] $₂ / €₂ } + @₂ $2 The motion of interest is a constant spin of B in N about an axis parallel to the orbit normal, i.e., ³ = @â₁ = nÒâ₁, for some given n. Select 7 appropriately to keep C fixed in A during the nominal motion. If r = x2, what is the proper choice of x? Why? What is the resulting particular solution of the differential equations that corresponds to the nominal motion? Demonstrate that it satisfies the differential equations.

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
8th Edition
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Kreith, Frank; Manglik, Raj M.
Chapter5: Analysis Of Convection Heat Transfer
Section: Chapter Questions
Problem 5.8P
See similar textbooks
icon
Related questions
Question
The problems are generally based on the following model: A particular spacecraft can be represented as a single axisymmetric rigid body B. Let n₂ be inertially fixed unit vectors; then, 6, are parallel to central, principal axes. To make the mathematics simpler, introduce a frame C where n₂ = ĉ₁ = b; initially. 6₁ Assume a mass distribution such that J =₁₁• B* •b₁ = 450 kg - m² I = b² •Ï¾˜ • b₂ = b¸ •Ï¾* •b¸ = 200 kg - m² K J-I C³ =r₁₁ = r₁₁
Transcribed Image Text:The problems are generally based on the following model: A particular spacecraft can be represented as a single axisymmetric rigid body B. Let n₂ be inertially fixed unit vectors; then, 6, are parallel to central, principal axes. To make the mathematics simpler, introduce a frame C where n₂ = ĉ₁ = b; initially. 6₁ Assume a mass distribution such that J =₁₁• B* •b₁ = 450 kg - m² I = b² •Ï¾˜ • b₂ = b¸ •Ï¾* •b¸ = 200 kg - m² K J-I C³ =r₁₁ = r₁₁
Assume that the body moves in a circular orbit at a constant rate Q. Let â₁ be orbit-fixed unit vectors where a₂ is directed from the orbit center to B*; then â³ is 90° from a₂ in the direction of motion and â₁ is parallel to the orbit normal. ده * The dependent variables in the differential equations that govern motion include the measure numbers ₁; the kinematic variables that are the body 1-3-2 angles for orientation of C in A: @₁ = 0 w₂ = -Kw₁₂-rw₁₂+3KQ² (c₁₂S¸ − c₁₁ ) (c₁₁₁ + §¸§₁ ) w₁ = Kw₁₂+rw₂ −3KQ² (c₁S₂c₁₂ + $₁₂S₁) c₁₂ Ġ₁ = [(@₁c¸ + @¸§¸ − rc³)/2] - Ω ė₁₂ = − (@₁ − 1 ) s³ + W₂cz - - Ò¸ = {[@¸¢¸ − r¢¸+@₂$¸ ] $₂ / €₂ } + @₂ $2 The motion of interest is a constant spin of B in N about an axis parallel to the orbit normal, i.e., ³ = @â₁ = nÒâ₁, for some given n. Select 7 appropriately to keep C fixed in A during the nominal motion. If r = x2, what is the proper choice of x? Why? What is the resulting particular solution of the differential equations that corresponds to the nominal motion? Demonstrate that it satisfies the differential equations.
Transcribed Image Text:Assume that the body moves in a circular orbit at a constant rate Q. Let â₁ be orbit-fixed unit vectors where a₂ is directed from the orbit center to B*; then â³ is 90° from a₂ in the direction of motion and â₁ is parallel to the orbit normal. ده * The dependent variables in the differential equations that govern motion include the measure numbers ₁; the kinematic variables that are the body 1-3-2 angles for orientation of C in A: @₁ = 0 w₂ = -Kw₁₂-rw₁₂+3KQ² (c₁₂S¸ − c₁₁ ) (c₁₁₁ + §¸§₁ ) w₁ = Kw₁₂+rw₂ −3KQ² (c₁S₂c₁₂ + $₁₂S₁) c₁₂ Ġ₁ = [(@₁c¸ + @¸§¸ − rc³)/2] - Ω ė₁₂ = − (@₁ − 1 ) s³ + W₂cz - - Ò¸ = {[@¸¢¸ − r¢¸+@₂$¸ ] $₂ / €₂ } + @₂ $2 The motion of interest is a constant spin of B in N about an axis parallel to the orbit normal, i.e., ³ = @â₁ = nÒâ₁, for some given n. Select 7 appropriately to keep C fixed in A during the nominal motion. If r = x2, what is the proper choice of x? Why? What is the resulting particular solution of the differential equations that corresponds to the nominal motion? Demonstrate that it satisfies the differential equations.
Expert Solution
steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Principles of Heat Transfer (Activate Learning wi…
Principles of Heat Transfer (Activate Learning wi…
Mechanical Engineering
ISBN:
9781305387102
Author:
Kreith, Frank; Manglik, Raj M.
Publisher:
Cengage Learning
International Edition---engineering Mechanics: St…
International Edition---engineering Mechanics: St…
Mechanical Engineering
ISBN:
9781305501607
Author:
Andrew Pytel And Jaan Kiusalaas
Publisher:
CENGAGE L
Mechanics of Materials (MindTap Course List)
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
Refrigeration and Air Conditioning Technology (Mi…
Refrigeration and Air Conditioning Technology (Mi…
Mechanical Engineering
ISBN:
9781305578296
Author:
John Tomczyk, Eugene Silberstein, Bill Whitman, Bill Johnson
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS